The Update of The Decomposition
One can proceed now to investigate the behaviour of the decomposition D when acted upon with one-qubit gates (OQG) and two-qubit gates (TQG) acting on neighbouring qubits. Instead of updating all the coefficients, we will restrict ourselves to a number of operations that increase in as a polynomial of low degree, thus saving computational time.
Read more about this topic: Time-evolving Block Decimation